# 线性代数作业代写linear algebra代考|Normal equation for a plane

my-assignmentexpert™ 为您的留学生涯保驾护航 在线性代数linear algebra作业代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的线性代数linear algebra代写服务。我们的专家在线性代数linear algebra代写方面经验极为丰富，各种线性代数linear algebra相关的作业也就用不着 说。

• 数值分析
• 高等线性代数
• 矩阵论
• 优化理论
• 线性规划
• 逼近论

## 线性代数作业代写linear algebra代考|collinear points

$$A=\left(x_{1}, y_{1}, z_{1}\right), B=\left(x_{2}, y_{2}, z_{2}\right), C=\left(x_{3}, y_{3}, z_{3}\right)$$ be three non-collinear points. Then the plane through $A, B, C$ is given by $$\overrightarrow{A P} \cdot(\overrightarrow{A B} \times \overrightarrow{A C})=0$$ or equivalently, $$\left|\begin{array}{ccc} x-x_{1} & y-y_{1} & z-z_{1} \ x_{2}-x_{1} & y_{2}-y_{1} & z_{2}-z_{1} \ x_{3}-x_{1} & y_{3}-y_{1} & z_{3}-z_{1} \end{array}\right|=0$$ where $P=(x, y, z)$.

## 线性代数作业代写linear algebra代考|symmetrical

Figure 8.17: The plane $a x+b y+c z=d$. REMARK 8.7.1 Equation $8.24$ can be written in more symmetrical form as $$\left|\begin{array}{cccc} x & y & z & 1 \ x_{1} & y_{1} & z_{1} & 1 \ x_{2} & y_{2} & z_{2} & 1 \ x_{3} & y_{3} & z_{3} & 1 \end{array}\right|=0$$ Proof. Let $\mathcal{P}$ be the plane through $A, B, C$. Then by equation $8.21$, we have $P \in \mathcal{P}$ if and only if $\overrightarrow{A P}$ is a linear combination of $\overrightarrow{A B}$ and $\overrightarrow{A C}$ and so by lemma 8.6.1(i), using the fact that $\overrightarrow{A B} \times \overrightarrow{A C} \neq 0$ here, if and only if $\overrightarrow{A P}$ is perpendicular to $\overrightarrow{A B} \times \overrightarrow{A C}$. This gives equation 8.23.

Equation $8.24$ is the scalar triple product version of equation $8.23$, taking into account the equations \begin{aligned} &\overrightarrow{A P}=\left(x-x_{1}\right) \mathbf{i}+\left(y-y_{1}\right) \mathbf{j}+\left(z-z_{1}\right) \mathbf{k} \ &\overrightarrow{A B}=\left(x_{2}-x_{1}\right) \mathbf{i}+\left(y_{2}-y_{1}\right) \mathbf{j}+\left(z_{2}-z_{1}\right) \mathbf{k} \ &\overrightarrow{A C}=\left(x_{3}-x_{1}\right) \mathbf{i}+\left(y_{3}-y_{1}\right) \mathbf{j}+\left(z_{3}-z_{1}\right) \mathbf{k} \end{aligned}

## 在这种情况下，如何学好线性代数？如何保证线性代数能获得高分呢？

1.1 mark on book

【重点的误解】划重点不是书上粗体，更不是每个定义，线代概念这么多，很多朋友强迫症似的把每个定义整整齐齐用荧光笔标出来，然后整本书都是重点，那期末怎么复习呀。我认为需要标出的重点为

A. 不懂，或是生涩，或是不熟悉的部分。这点很重要，有的定义浅显，但证明方法很奇怪。我会将晦涩的定义，证明方法标出。在看书时，所有例题将答案遮住，自己做，卡住了就说明不熟悉这个例题的方法，也标出。

B. 老师课上总结或强调的部分。这个没啥好讲的，跟着老师走就对了

C. 你自己做题过程中，发现模糊的知识点

1.2 take note

1.3 understand the relation between definitions